1. Porous media equationWe considerd the Cauchy problem of the porous media equation. We showed that its spherically symmetric solution has the same property as Barenblatt so1ution, with respect to some regularity property.2. Equation of linear elastostatics (joint work with K.Wada)The equation of linear elastostatics was treated in the famous book of Duvaut and Lions, where the existence and the uniqueness off solutions were shown under discontinuous boundary condition. We proved some regularity property for these solutions.本研究ではUが球対称解で、1<m<3かつN=1,2,3のとき、U_0にある仮定をおけば、Uは上記のBarenblatt解の性質をもつことを示した。